This invention claims priority of a German patent application DE 100 11 201.3 which is incorporated by reference herein.
The invention concerns the field of electron beam lithography, and in particular a method and an apparatus for forming, with the aid of an electron beam, a polyline on a substrate coated with a radiation-sensitive resist, the electron beam being directed onto the coated substrate surface in the direction of the Z coordinate, and the substrate being displaced stepwise in the direction of the X and/or Y coordinate of a Cartesian grid while the electron beam acts with a predefined energy on the resist.
Apparatuses for electron beam lithography comprise a radiation source for emitting a collimated electron beam that is directed onto a substrate coated with a radiation-sensitive resist. The substrate, with a surface that bears the resist layer and is oriented perpendicular to the electron beam, is placed onto a stage displaceable in a Cartesian grid and is held thereon. As a result of predefined stage displacement or electromagnetic deflection of the electron beam, or both simultaneously, the impact point of the electron beam being modified with respect to the substrate surface in defined fashion, geometrical structures or patterns, in particular polylines, are written into the resist.
This principle of relative motion between the substrate and the electron beam by displacement of the substrate stage with respect to an at least approximately stationary electron beam is known, for example, from Microelectronic Engineering (1995) 135-138. An alternative possibility for controlled modification of the impact point on the substrate surface consists in deflection of the electron beam, for example by means of electromagnetic deflection systems.
Since apparatuses of this kind for positioning the substrate stage or the electron beam generally use a Cartesian coordinate system with X and Y coordinates, the data description of the geometrical structures to be constituted on the substrate is also preferably embodied in Cartesian coordinates. These are well-suited to the description of structures of predominantly rectangular or trapezoidal shape, such as are typically used in microelectronics. The straight polylines which usually occur in this context can be transferred onto the substrate with little edge roughness using positioning devices controlled in stepwise fashion.
In particular when exposing substrates that are intended for optical applications, however, it is of great interest also to write curved polylines with high accuracy, for example in order to be able to produce elliptical gratings, circular gratings, or even curved waveguides. When a Cartesian grid is used, polylines of this kind can be approximated at best with the accuracy of the individual increments of suitable positioning devices in their X and Y coordinates. If the individual increment distance is selected to be sufficiently small with respect to the width of the desired polyline, it is possible to ignore the edge roughness caused by the stepwise approximation and the geometrical deviation of the approximate polyline from a theoretically ideal polyline.
As a result of stage displacement in incremental steps, a polyline is formed on a substrate by close juxtaposition of a plurality of irradiation points. In order to irradiate a point, the electron beam remains directed onto the point in question for a short dwell time, until a desired energy input has been reached. The beam then moves to the next point, and the same operation is performed. It is not absolutely necessary, in this context, to switch off the electron beam between immediately successive points. The level of energy input onto the location where the electron beam strikes the resist yields a smaller or larger exposed xe2x80x9cspotxe2x80x9d on the resist.
For the formation of polylines with a very narrow line width that is nevertheless as uniform as possible, it is therefore very important to keep the energy input into the electron-sensitive resist, i.e. the effective dose (charge per unit area) or effective linear dose (charge per unit length) as constant as possible along the polyline. Unlike the edge roughness, the width fluctuations along the polyline that otherwise occur cannot be eliminated by decreasing the individual steps for positioning of the substrate with respect to the electron beam.
A positioning device operated stepwise in the X and Y coordinates makes possible both paraxial individual steps in which progress occurs one individual increment at a time in only one of the X or Y coordinates, or individual steps in which an advance is made in both the X coordinate and the Y coordinate. It is apparent that in the latter case, the spacing between the starting point and end point of the individual step is greater than in the case of a paraxial individual step. If the individual increments in the two coordinates X and Y are identical, there is then a length increase by a factor of 2.
Thus if an identical energy input is provided after each individual step, the result is then a higher linear dose for a paraxial polyline in the X or Y coordinate direction than for a diagonal polyline in the direction of a line inclined 45xc2x0 to the X or Y coordinate. This difference in energy input is expressed as a deviation in line width, so that the diagonal polyline has a narrower width than the paraxial polyline.
If, on the other hand, an energy input elevated by a factor of 2 is permanently defined, the result is an excessive linear dose in terms of the line that is to be generated paraxially, since the track length is shorter than in the case of the inclined line. A quantitative calculation shows that in the case presently under consideration, the discrepancy is greatest at an angle of 22.5xc2x0, and equals approximately 8%. It would theoretically be possible to decrease this discrepancy by adjusting the energy input for a line as a function of angle, but this would entail a considerably greater calculation effort.
For curved polylines, in particular for circular lines, the path angle continuously changes. Separate calculation of the energy input after each individual step would result in an enormous increase in calculation effort, and therefore drastically decrease the working speed when writing a curved line. This procedure of determining the exact energy input as a function of the instantaneous slope of the polyline after each individual step is therefore unsatisfactory in terms of efficient production. On the other hand, it is precisely in the context of circular gratings that the dose fluctuations resulting from approximation become particularly clearly perceptible, so that it is of interest to remedy this situation.
It is therefore the object of the present invention to develop the known method for electron beam lithography so as to make possible the formation of curved polylines with a uniform line width and little calculation effort.
According to the present invention, in a method of the kind described initially, the energy to be defined is determined after each individual step as a function of the shape of the polyline ascertained from several preceding individual steps.
The result of this is to achieve an energy input into the resist which is adapted to the greatest possible extent to the shape of the polyline, so that polylines curved in any desired fashion can be produced with a very uniform line width. Because several preceding individual steps are taken into consideration, data concerning the shape of the polyline that have already been acquired or calculated are utilized to determine the energy input after the most recently performed individual positioning step. The calculation effort necessary for this is considerably less than separate calculation of the theoretically exact energy input based on a description of the polyline shape in conjunction with performance of an individual step. This consideration of the past history of each individual step can be implemented essentially with no reduction in working speed.
The fundamental principle of the method according to the present invention consists in defining a number of categories of individual steps, each of which has assigned to it a specific correction factor for the purpose of determining the energy input in the context of an individual step that will follow later. It is advisable in this context to weight the correction factors assigned to the categories of different individual steps in accordance with the respective shortest path length between the starting point and end point, and to assign individual steps having the same weighting to one respective category.
In a preferred embodiment of the method, only two categories of individual steps are used, namely a first category A of paraxial individual steps in the form of individual increments in the direction of the X coordinate or the Y coordinate, and a second category B of diagonal individual steps in the form of an individual increment in both the X and the Y coordinate.
The individual steps of category A are assigned a correction factor of 1, and those of category B a correction factor of 2. Determination of the energy input for a subsequent individual step is accomplished, according to the present invention, as a function of a number of previously completed individual steps in category A and in category B. Because of the orientation toward the individual increments in the X and Y coordinates and the small number of different types of individual steps, the control and calculation outlay associated with application of the method remains low. A highly uniform profile is nevertheless achieved for the effective linear dose (and thus for the line width) along a trajectory of any desired curvature, regardless of its path angle.
A particularly low calculation effort is achieved, for example, if eight immediately preceding individual steps are considered, and if an average correction factor Kn is determined in accordance with an allocation protocol as a function of the number of individual steps in categories A and B, as discussed below.
It is nevertheless certainly possible to reduce the number of individual steps that are considered retrospectively as necessary or, in order to improve accuracy further, to increase it. The hardware and calculation outlay rises, however, with an increasing number of individual steps to be considered. Individual steps that are far in the past may furthermore result in an incorrect determination of the average correction factor Kn. Taking this problem into account, a consideration of eight preceding individual steps has proven particularly advantageous. The energy input is preferably made in proportion to the calculated average correction factor Kn.
In the context of a consistent radiation output, the energy input is adjusted, by way of the application duration of the electron beam for each individual step, in proportion to the correction factor Kn. This procedure has the advantage that a field emission cathode, which is notable for its extraordinarily uniform radiation output in steady-state operation, can be used as the radiation source. The application duration is defined by the halt time of the stage positioning device after an individual step. The time interval during which the stage remains in position after an individual step has been performed is consequently proportional to the average correction factor Kn.
In an alternative embodiment of the method, the energy input is made by modifying the radiation output in the context of a consistent application duration or constant halt time. This has the advantage that stage displacement can be effected with no change in the working cycle. If a field emission cathode is used as the radiation source, however, it is not advisable to modify its radiation output during operation, since the radiation output adapts only very slowly to any change in an applied voltage. Instead, in order to influence the energy input, the electron beam emitted from the radiation source is attenuated downstream, for example using an air coil. The first-mentioned variant with a variable halt time is preferable in this regard.
The object of the invention is furthermore achieved with an apparatus for forming a polyline on a substrate coated with a radiation-sensitive resist with the aid of an electron beam, comprising a radiation source for irradiating the substrate with an electron beam in the direction of a Z coordinate; a positioning device, movable in individual steps in an X-Y plane in order to effect a relative motion between the substrate and the electron beam; and a calculation circuit for ascertaining the energy to be defined for a respective individual step as a function of the shape of the polyline ascertained from several preceding individual steps, the calculation circuit being connected to the activation circuit for the radiation source.
The apparatus according to the present invention makes possible application of the method explained above for generating a polyline of any desired curvature, with an energy input into the resist adapted to the greatest possible extent to the shape of the polyline and thus with a consistent line width.